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3 years ago

Find the surface area of the prism. 12 in. 6 in. 5 in. The surface area is in.2.

Mathematics

1 answer:

Ber [7]3 years ago

8 0

Answer:

324

Step-by-step explanation:

SA = 2 ( lw + hl + hw )

l = length

w = width

h = height

<u>Given Dimensions</u>

l = 6

w = 5

h = 12

* plug in to SA formula *

SA = 2 ( (6)(5) + (12)(6) + (12)(5) )

(6)(5) = 30

(12)(6) = 72

(12)(5) = 60

SA = 2 ( 30 + 72 + 60 )

30 + 72 + 60 = 162

SA = 2(162) = 324

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I need to solve the equation please help me

lesantik [10]

Answer:

$\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}$

Step-by-step explanation:

We are given the equation:

$4\sin^2(x)+6\sin(x)+2=0$

First, we can divide everything by 2:

$2\sin^2(x)+3\sin(x)+1=0$

Notice that we have an equation in quadratic form. Namely, if we make a substitution where u = sin(x), we acquire:

$2u^2+3u+1=0$

Solve for u. Factor:

$(2u+1)(u+1)=0$

Zero Product Property:

$2u+1=0\text{ or } u+1=0$

Solving for both cases:

$\displaystyle u=-\frac{1}{2}\text{ or } u=-1$

And by substitution:

$\displaystyle \sin(x)=-\frac{1}{2}\text{ or } \sin(x)=-1$

For the first case, recall that sin(x) is -1/2 for every 7π/6 and every 11π/6. Hence, for the first case, our solutions are:

$\displaystyle x=\frac{7\pi}{6}+2n\pi \text{ and } x=\frac{11\pi}{6}+2n\pi, n\in\mathbb{Z}$

Where n is an integer.

For the second case, sin(x) is -1 for every 3π/2. Thus:

$\displaystyle x=\frac{3\pi}{2}+2n\pi$

All together, our solutions are:

$\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}$

4 0

3 years ago

I need the answer to the image

Levart [38]

Answer:

∠B = 156°

Step-by-step explanation:

A line intersects two parallel lines this means that their opposite angles are transversals specifically the angles, A and B. And transversal angles are congruent so I can make this claim below:

$∠A = ∠B \\ 8x +78 = 2x +144$

Solving for x:

$8x +78 = 2x +144 \\ 8x -2x +78 = 2x -2x +144 \\ 6x +78 -78 = 144 -78 \\ 6x = 66 \\ \frac{6x}{6} = \frac{66}{6} \\ x = 11$

Solving Angle B if x = 11.

$∠B = 2x +144 \\ ∠B = 2(11) +144 \\ ∠B = 22 +144 \\ ∠B = 166$

7 0

4 years ago

$4500 at 5.5% for 4/1/2 Year’s

AnnyKZ [126]

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25.5 is what percent of 60

OLEGan [10]

%/100 = is/of
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4 years ago

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A person eating at a cafeteria must choose 4 of the 13 vegetables on offer. calculate the number of elements in the sample space

Serggg [28]

A person eating at a cafeteria must choose 4 of the 13 vegetables on offer. calculate the number of elements in the sample space for this experiment.

Answer: The number of elements in the sample space for this experiment can be found using the combination formula because the order does not matter here.

Therefore, the number of elements in the sample space for this experiment is:

$13C4=\frac{13!}{(13-4)!4!}$

$=\frac{13!}{9! \times 4!}$

$=\frac{6227020800}{8709120}$

$=715$

Therefore, the number of elements in the sample space for this experiment is 715.

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4 years ago